Algorithmic information theory and undecidability

Synthese 123 (2):217-225 (2000)
Abstract
Algorithmic information theory, or the theory of Kolmogorov complexity, has become an extraordinarily popular theory, and this is no doubt due, in some part, to the fame of Chaitin’s incompleteness results arising from this field. Actually, there are two rather different results by Chaitin: the earlier one concerns the finite limit of the provability of complexity (see Chaitin, 1974a, 1974b, 1975a); and the later is related to random reals and the halting probability (see Chaitin, 1986, 1987a, 1987b, 1988, 1989.
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Mihai Ganea (2008). Epistemic Optimism. Philosophia Mathematica 16 (3):333-353.
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